The invention relates to an inverter based power source which has a waveform generator or wave shaper controlling a pulse width modulator for generating the shape of various portions in an AC welding cycle. A unique control system for this type of welder and method is shown in Houston U.S. Pat. No. 6,472,634. This patent is incorporated by reference herein. The individual AC waveforms obtained by using the control system and welder disclosed in Houston U.S. Pat. No. 6,472,634 constitute unique technology where a number of current pulses occur at a frequency of at least 18 kHz, with a magnitude of each current pulse controlled by the wave shaper or waveform generator. Such waveform technology dates back to Blankenship U.S. Pat. No. 5,278,930, which discloses the shaping of the waveform in an AC welding method. This early creation of AC waveforms for electric arc welding was primarily used for solid welding wires. There has been suggestion that an AC waveform obtained by an inverter using a waveform generator or wave shaper could be adapted for use with cored electrodes. By specially constructing the AC waveform, the waveform can be coordinated with a specific cored electrode so the sheath and core burn back at a desired rate. In this manner, it has been found that AC welding can be used successfully for cored electrodes. In the past, normally DC welding was used for cored electrodes. By creating a specific profile for an AC waveform, the overall welding process is tailor made for use with a cored electrode; however, this type of coordination of the AC waveforms with a cored electrode required very accurate waveform creation. This objective has been obtained only by using waveform technology of the type pioneered by The Lincoln Electric Company of Cleveland, Ohio. By accurately controlling the AC waveform used with the cored electrode, characteristics of the welding process, such as penetration into the base metal, melt off rate of the electrode, the heat input to the base metal, and the welding travel time, as well as the wire feed speed, is optimized. The creation of accurately controlled AC waveforms for use with specific cored electrodes is not a prior art concept, but is the general background to which the present invention is directed.